Atleti bagged its first league title in 18 years in the 2013-14 campaign, stunning favorites Barcelona and Real Madrid, while Simeone's men also came within seconds of winning the Champions League.
While Atletico's La Liga success was considered one of the fairytale stories of last season across Europe, Simeone — who has been in charge at the Vicente Calderon since December 2011 — said it had been coming.
The Vicente Calderon side won the Europa League in 2012, while it also claimed the UEFA Super Cup after each of the aforementioned titles, as well as scooping up the 2013 Copa del Rey.
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"Last year was no fluke, it was a consequence of what has been going on at the club," Simeone told AS. "First it was [winning] the Europa League, then the European Super Cup, Copa del Rey, third in the league and the following year the Liga title and the Champions League final."
Simeone said that with the additions of Mario Mandzukic, Antoine Griezmann and Jan Oblak, plus the retention of a large chunk of last season's squad, there is no reason Atletico cannot challenge the likes of Real and Barca again.
"The technical department have been working through all of this during the past 40 days," he said. "Filipe Luis left and Guilherme Siqueira came in; Thibaut Courtois has gone while Miguel Angel Moya and Oblak are now onboard; up front we've lost Diego Costa and Mandzukic has arrived.
"Griezmann will give us the velocity we've lacked and needed. You don't create a team from just 11 players but from 18 or 20."